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arXiv · 2511.22192

Ergodic distribution dependent BSDE and application to long-time behavior of finite horizon distribution dependent BSDE

Kaplan Desbouis·Adrien Richou
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Abstract

After proving existence and uniqueness of ergodic distribution dependent backward stochastic differential equations (BSDEs) under strong and weak dissipativity regimes for the underlying McKean--Vlasov SDE, we leverage this new framework to investigate the long-time behavior of distribution dependent BSDEs on a finite-time horizon. Finally, we apply our results to solve an ergodic McKean--Vlasov stochastic control problem and study the long-time behavior of the value function of a finite-horizon McKean--Vlasov stochastic control problem.

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Kaplan Desbouis, Adrien Richou. 2025-11-27. Ergodic distribution dependent BSDE and application to long-time behavior of finite horizon distribution dependent BSDE. https://arxiv.org/abs/2511.22192

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